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Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988,

Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1), 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe") is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional understanding of heat- work efficiency. It is concluded that the intuitively derived assumptions over the last two centuries seem to be reasonably well grounded, requiring perhaps some minor elaboration to the concepts of (i) system, (ii) the mechanism of heat transfer, and (iii) the environment, which would be expected to evolve with time in any case. If new generalizations at variance with Clausius' concepts are presented, then these ideas could be expected to require a different axiomatic basis than the one for equilibrium theory, and this difference must be stated at the outset of any new development. So far such empirically self-consistent axiomatic developments are not very much in evidence.
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Many quantitative measures of the degree of chirality or symmetry of a set have been proposed in the literature. The main approaches from various areas are reviewed: chemistry, physics, mathematics, computer sciences, biology, and psychophysics. Relations between chirality, symmetry, and other concepts such

Many quantitative measures of the degree of chirality or symmetry of a set have been proposed in the literature. The main approaches from various areas are reviewed: chemistry, physics, mathematics, computer sciences, biology, and psychophysics. Relations between chirality, symmetry, and other concepts such as similarity, disorder and entropy, are discussed.
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